Diagram Kendali T2 Hotelling Sintetik dengan Parameter in Control dalam Interval Kecil

Friska Aulia Resky, Suwanda Suwanda

Abstract


Abstract The T2 Hotelling control chart is a class of Shewhart control diagrams, so it is less sensitive in detecting small mean vector shifts. To overcome this, a synthetic T2  Hotelling control chart was created, which is a combination of the T2 Hotelling control chart and the Conforming Run Length (CRL) control chart. In this way, the synthetic T2 Hotelling control chart is expected to be sensitive in detecting small changes in the process mean vector while maintaining good performance. If it is true that there is a shift in the average vector in the process, the Average Run Length (ARL) becomes a minimum, but if there is no shift in the average vector ARL becomes a maximum. In this thesis discusses the synthetic T2 Hotelling control chart for cases where in a state of control the magnitude of the shift is at a set interval, so as to get the upper control limit for the T2 Hotelling control chart (BKAsin) and the lower control limit for the CRL control chart (Lsin) sub. Obtained from the multi-object optimization case. This can be solved by the Pareto-optimal approach using the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). This control chart is applied to controlling  the production process of making yarn where using d = B = 1.5 and d = 0 to d = A = 0.1, the ARL value (d = 0) is 88.0121, ARL (d = A) is 38.1111 and ARL (d = B) is 1.57974 while for the BKAsin value of 6.98528 and the Lsin value  is 2 , from these values it is concluded that by using the Synthetic Hotelling T2 Control chart there has been an average vector shift in the 6th observation so that the yarn production process is said to be out of control

Keywords: T2 Hotelling control chart, CRL control chart, Synthetic control chart, Multi-Object Optimization, Pareto Optimal.

Abstrak. Diagram kendali T2 Hotelling merupakan kelas diagram kendali Shewhart, sehingga kurang peka dalam mendeteksi pergeseran vektor rata-rata yang kecil. Untuk penanggulangannya dibuat  diagram kendali T2 Hotelling sintetik, yaitu gabungan dari diagram kendali T2 Hotelling dan diagram kendali Conforming Run Length (CRL). Dengan cara ini, diagram kendali T2 Hotelling sintetik diharapkan dapat peka dalam  mendeteksi perubahan kecil dalam vektor rata-rata proses dan tetap menjaga perfomansi dengan baik. Jika benar terdapat pergeseran vektor rata-rata pada proses, Average Run Length (ARL) menjadi minimum akan tetapi jika tidak terdapat pergeseran vektor rata-rata ARL menjadi maksimum. Dalam penelitian ini membahas diagram kendali T2 Hotelling sintetik untuk kasus dimana dalam keadaan in control besarnya pergeseran berada pada interval yang ditetapkan, sehingga untuk mendapatkan batas kendali atas untuk sub diagram kendali T2 Hotelling (BKAsin) dan batas kendali bawah sub diagram kendali CRL (Lsin) diperoleh dari kasus optimasi multi-objek. Hal ini dapat diselesaikan oleh pendekatan Pareto-optimal menggunakan Non-dominated Sorting Genetic Algorithm-II (NSGA-II). Diagram kendali ini, diaplikasikan pada pengontrolan proses produksi pembuatan benang dimana dengan menggunakan d=B=1.5 dan d=0 sampai dengan d=A=0.1 didapatkan nilai ARL(d=0) sebesar 88.0121, ARL(d=A) sebesar 38.1111 dan ARL(d=B) sebesar 1.57974 sedangkan untuk nilai BKAsin sebesar 6.98528 dan nilai Lsin 2, dari nilai-nilai tersebut disimpulan bahwa dengan menggunakan diagram Kendali T2 Hotelling Sintetik telah terjadi pergeseran vektor rata-rata pada pengamatan ke-6 sehingga proses produksi benang dikatakan out of control

Kata Kunci: Diagram kendali T2 Hotelling, Diagram kendali CRL, Diagram kendali Sintetik, Optimasi Multi-Objek, Pareto Optimal.


Keywords


Diagram kendali T2 Hotelling, Diagram kendali CRL, Diagram kendali Sintetik, Optimasi Multi-Objek, Pareto Optimal.

Full Text:

PDF

References


Aditama, Darmawan. (2017). Evolusi Dinamis Perilaku Non-Player Character Pada Game Space Shooter Menggunakan NSGA-II. Surabaya. Tesis tidak dipublikasikan. Program Magister, Program Studi Teknik Elektro, Institut Teknologi Sepuluh Nopember.

Aparisi, Francisco and Marco, A de Luna (2007). The Synthetic Contorl Chart and its Multi-Objective Optimization. Engineering and Technology 11, 225-228.

Bourke, P. D. (1991). Detecting a Shift in Fraction Nonconforming Using Run Length Control Charts with 100% Inspection. J. Qual. Technol. 23(3), 225-238.

Chen, F. L & Huang, H. J. (2005). A Synthetic Control Chart for Detetcting Small Shifts in the Process Mean. Journal of Computers & Industrial Engineering 49(2).221-240.

Deb, K. (2001). Multi-Objective Optimization Using Evolutionary Algorithms.New York : John Wiley and Sons.

Deb, K, Pratap, A, Argawal , S, & Meyarivan, T. (2002). A fast elitist multiobjective genetic algorithm:NSGA-II, IEEE Trans Evol Comput, 182-97.

Isnaeni, Sherly. (2015). Penerapan Algoritme Genetika Multi-Objective NSGA-II Pada Optimasi Portofolio Saham. Journal Of Engineering Proceeding .2(2), 6841-6850.

Johnson, Richard. Dean Wichern. (2007). Applied Multivariat Statistical Analysis, 5th ed. New Jersey: Prentice Hall.

Montgomery, D.C.(2005). Introduction to Statistical Quality Control. 5th ed. New York : John Wiley and Sons.

Montgomery, Douglas C.(1990). Pengantar Pengendalian Kualitas Statistik. Yogyakarta : Gajahmada University Press

V.B.Ghute & D.T. Shirke (2008): A Multivariat Synthetic Control Chart for Monitoring Process Mean Vektor. Communications in Statistic-Theory and Methods ,37:13, 2136-2148.

Woodall, W. H.(1985). The Statistical Design of Quality Control Charts. Journal of the Statistician 34, 647-657.




DOI: http://dx.doi.org/10.29313/.v6i2.23123

Flag Counter